"There was no distress," Keevill told reporters at a press conference on Friday.
"When [Bedell] reached into his pocket, they assumed he was going to get a pass and he came up with a gun. He wasn't pretending to be anyone. He was wearing a coat and walked up and just started shooting.
'No terrorist connections'
Keevill said "layers of security" at the Pentagon helped foil the attack and prevent the man from entering the building.
Meanwhile, the two officers wounded in the attack have been released from hospital after being treated for "superficial injuries".
Officials said they are investigating a motive for the attack but they said the man appeared to have been acting alone with no links to terrorism.
"There is no indication at this point that there are any domestic or international terrorist connections at all," Keevill said.
But he said authorities are probing a series of postings on the Internet by a user identified as "JPatrickBedell" for clues.
The postings make reference to the September 11, 2001, attacks against the United States and the case of a US Marine Corps colonel who died in 1991.
In one such post, the user named JPatrickBedell wrote that he was "determined to see that justice is served" in the death of Marine Colonel James Sabow, who was found dead at his California home in 1991.
The death was ruled a suicide but the case has long been the source of theories of a cover up.
The user named JPatrickBedell wrote that the Sabow case was "a step toward establishing the truth of events such as the September 11 demolitions".
Nearly 3,000 people were killed at the World Trade Centre in New York, the Pentagon in Virginia and in a field in Pennsylvania during the co-ordinated attacks of September 11.